Geodesic
Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states
ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 2, pp. 237-264

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This paper studies Monge parameterization, or differential flatness, of control-affine systems with four states and two controls. Some of them are known to be flat, and this implies admitting a Monge parameterization. Focusing on systems outside this class, we describe the only possible structure of such a parameterization for these systems, and give a lower bound on the order of this parameterization, if it exists. This lower-bound is good enough to recover the known results about “(x,u)-flatness” of these systems, with much more elementary techniques.

DOI : 10.1051/cocv:2007011
Classification : 93B18, 93B29, 34C20
Keywords: dynamic feedback linearization, flat control systems, Monge problem, Monge equations 
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     author = {Avanessoff, David and Pomet, Jean-Baptiste},
     title = {Flatness and {Monge} parameterization of two-input systems, control-affine with 4 states or general with 3 states},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {237--264},
     publisher = {EDP-Sciences},
     volume = {13},
     number = {2},
     year = {2007},
     doi = {10.1051/cocv:2007011},
     mrnumber = {2306635},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2007011/}
}
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Avanessoff, David; Pomet, Jean-Baptiste. Flatness and Monge parameterization of two-input systems, control-affine with 4 states or general with 3 states. ESAIM: Control, Optimisation and Calculus of Variations, Tome 13 (2007) no. 2, pp. 237-264. doi: 10.1051/cocv:2007011

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